I am using false time step factors for calculating unsteady 3D multi-fluid flow in a wwtp aeration tank. I am using false time step factors to avoid numerical instability. My problem is that I canīt find any good definition of what false time steps exactly do, or how it works. The CFX 4.4 manual doesn't give any usefull information on that point. Can anyone give me a thorough description of how it works? -Or do anybody know any good articles on the subject? Are there any drawbacks in using false time step factors in the problem described above?

Thanks in advance Jesper, a student from Denmark.

Adarsh

June 1, 2002 02:35

Re: False time step factors

hello Jesper my work is somewhat similar to urs.... i think this cud be useful for u A.Jameson -AIAA paper -1991-"time dependent calculations.....".. he also uses false time stepping for unsteady flows .. though i am still to get what exactly he does.. still we can discuss . you can choose to write to me at chugh@aero.iisc.ernet.in personally.

regards, Adarsh

Rami

June 2, 2002 03:04

Re: False time step factors

Hi Jesper,

False time steps is a numerical relaxation technique used to stabilize the solution. It does so by adding a pseudo-transient term to the solved conservation equation, and then advances the iterative process by time increments.

The time increment size is usually based on the CFL (Courant-Friedrichs-Levy) stability condition. This condition varies from one scheme to another. A rough estimate would be dt < min{(cell size)/velocity} over the entire grid. However, implicit schemes may usually maintain stability with much larger (x5 or so) steps.

This type of process is usually applied for steady problems in which the time-stepping is merely used as intermetiate iteration, therefore the time steps may be chosen to satisfy the CFL condition locally, i.e., advancing the solution at each computational grid using a different false-time-step, which is calculated based on the cell size and velocity, rather than the minimal value of the whole grid. This is in contrast to solution of transient problems, where the solution should be advanced using a uniform step, and it is therefore the minimal value over the entire grid (hence the term "false").

The drawback of the method is related to the stabilty limit: on certain occasions many steps are required to obtain convergence.

you have given an eloquent description of false time steps.. which is done for faster convergence .. but if we want to obtain the time accurate solutuion then time steps must be equal(as you have said) .. is false time stepping still apllicable .. if yes, i what manner. becos the minimum time step then wud be determined by lowest CFL ...

Jameson has done some false time stepping for time accurate solutions..in his work (aiaa-1991) ..where he runs one additional pseudo loop for each time step to obtain convergence .. it will be kind of you to highlight something more on this topic .. also suggest me some other book or paper.. the book by tennihill and pletcher is not availbale here at my institute.. thanks in advance regards, adarsh

Rami

June 4, 2002 04:35

Re: False time step factors

Dear Adarsh,

I agree with you that when a time-accurate (i.e., transient) solution is sought you should advance the solution with the same time step throughout the grid (unless you use some time-interploation, which seems to be complex approach to me). Therefore, the minimal time-step (as determined by the CFL criterion) should be applied. In that case, the term "false" seems inappropriate to me, as this is physically meaningful time incrementing.

I cannot recommend off-hand any other book other than Anderson et al, but I assume you will find it in any CFD textbook (e.g., Hirsch).